Problem detail · source-aware
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Bondal and Polishchuk conjectured in 1993 that the braid group acts transitively on the set of full exceptional collections in a triangulated category. Chang, Haiden and Schroll disproved it for partially wrapped Fukaya categories, but no counterexample of the form $D^b(X)$ for a smooth projective variety was known. A particular weak Fano threefold provides one.
The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.
The AI disclosure is carefully bounded and worth quoting in full: the model most significantly found numerous mistakes in earlier attempted constructions, leading to the successful modifications, and it located the reference containing the threefold used. The author states that it did not produce the actual counterexample and was not used to generate any of the text.
Provider: OpenAI · Prompt public: unknown · Independence: unknown
Single-author arXiv preprint; not yet peer-reviewed.
Correctness: unknown · statement fidelity: unaudited · peer review: none
first counterexample of the form D^b(X) for X smooth projective
Source-reported tools: construction.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.